where \(p_{*,i}^{select}\)  is the prior probability that item \(i\)  is recommended by the deployed model and \(p_{*,i}^{interact|select}\)  is the conditional probability that the user interacts with item \(i\)  given that it is recommended.
Based on a set of mild assumptions, we can estimate the user independent propensity score \(p_{*,i}\)  as follows [1]}:
\(\hat{p}_{*, i} \propto \left(n_{i}^{*}\right)^{\left(\frac{\gamma +1}{2}\right)}\) 
